Yulan absolutely remembers the previous loop, and it's implied he's responsible for time going back, see, when Violette was sentenced to jail, he got pissed because he knew her past and how she was really like, but that no one ever gave her a fair shake and that she was now going to spend the rest of her life in terrible conditions, and he planned to break her out of there but never could.
And at one point he went to a church and spent a lot of time praying to God so that he would save Violette, so that there would be a miracle, anything that would allow him or someone to save her and it's implied that God felt moved by his dedication and love and granted a miracle, both went back in time but didn't know each other did as well.
Yulan went in wanting to get more power and influence, and interact with Violette so he could change the future and better protect her, but much to his suprise, she seemed different, but i don't know if he realizes that Violette also went back in time.